1
Morphogenetic Robotics: An Emerging New Field
in Developmental Robotics
Yaochu Jin, Senior Member, IEEE, and Yan Meng, Member, IEEE
Abstract— Developmental robotics is also known as epigenetic
robotics. We propose in this paper that there is one substantial difference between developmental robotics and epigenetic
robotics, since epigenetic robotics concentrates primarily on
modeling the development of cognitive elements of living systems
in robotic systems, such as language, emotion, and social skills,
while developmental robotics should also cover the modeling of
neural and morphological development in single and multiple
robot systems.
With the recent rapid advances in evolutionary developmental
biology and systems biology, increasing genetic and cellular
principles underlying biological morphogenesis have been revealed. These principles are helpful not only in understanding
biological development, but also in designing self-organizing,
self-reconfigurable and self-repairable engineered systems. In
this paper, we propose morphogenetic robotics, an emerging
new field in developmental robotics, is an important part of
developmental robotics in addition to epigenetic robotics. By
morphogenetic robotics, we mean a class of methodologies in
robotics for designing self-organizing, self-reconfigurable, and
self-repairable single- or multi-robot systems using genetic and
cellular mechanisms governing biological morphogenesis. We
categorize these methodologies into three areas, namely, morphogenetic swarm robotic systems, morphogenetic modular robots
and morphogenetic body and brain design for robots. Examples
are provided for each of the three areas to illustrate the main
ideas underlying the morphogenetic approaches to robotics.
Keywords: Morphogenesis, morphogenetic robotics, epigenetic
robotics, developmental robotics, evolutionary developmental
robotics
I. W HAT IS AND W HY M ORPHOGENETIC ROBOTICS ?
Developmental robotics is an interdisciplinary field of
robotics that employs simulated or physical robots to understand natural intelligence on the one hand, and to design better
robotic systems using principles in biological development, on
the other hand [57]. The term developmental robotics is often
used interchangeably with other two terms, namely epigenetic
robotics [64] and ontogenetic robotics, which focuses on
modeling the postnatal development of cognitive behaviors in
living systems, such as language, emotion, anticipation, and
social skills. Note, however, that the meaning of epigenetic
is not unambiguous in biology. It can either be derived
from epigenesis that describes morphogenesis and postnatal development of organisms, or from epigentics referring
to the changes in gene expression that are not caused by
genetic changes. Although the difference between developmental robotics and epigenetic robotics has been noticed
Yaochu Jin is with the Department of Computing, University of Surrey,
Guildford, Surrey, GU2 7XH, UK. Email: [email protected].
Yan Meng is with the Department of Electrical and Computer Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA. Email:
[email protected].
and topics that are far beyond cognitive development have
been discussed [57], researchers have so far refrained from
stressing the difference between developmental robotics and
epigenetic robotics. Nevertheless, other terminologies such as
developmental cognitive robotics [50], and autonomous mental
development [95] have also been suggested to refer to the
research efforts on modeling cognitive development, which we
believe may be seen as attempts to clarify the confusion caused
by treating epigenetic robotics equivalent to developmental
robotics.
The physical development of animals includes the processes
that cause the creation of both the body plan and nervous
system, including cleavage, gastrulation, neurulation, organogenesis [96]. Some living organisms, such as amphibians, also
undergo a biological process known as metamorphosis, during
which both the shape and size of the organisms change [9].
The past decade has witnessed rapid technical and theoretical
advances in evolutionary developmental biology [28] (often
known as evo-devo) and systems biology in understanding
molecular and cellular mechanisms that control the biological
morphogenesis. These advances have not only helped us in understanding biological processes such as human deceases, but
also provided us new powerful tools for designing engineered
systems. For example, increasing evidence has been revealed
that biological morphogenesis can be regarded as a selforganizing and self-assembling process through cellular and
molecular interactions under the genetic and environmental
control [6], [86]. In addition, biological morphogenesis has
also shown a surprising degree of robustness [7]. Due to the
attractive properties that biological morphogenesis exhibits,
much attention has been paid to employing genetic and cellular
mechanisms for designing robotic systems, in particular for
self-organizing swarm robotic systems and self-reconfigurable
modular robots. In addition, a large body of research has been
performed in artificial life and robotics to design the body
plan and neural controller of robots using an evolutionary
developmental approach [87], [89], [92].
In this article, we propose that it is high time that the difference between developmental robotics and epigenetic robotics
be stressed. To this end, we suggest that a new term, namely
morphogenetic robotics, be used to denote research efforts
dedicated to the application of morphogenetic mechanisms to
robotics, which belongs to developmental robotics. From our
perspective, morphogenetic robotics may include, but is not
limited to the following three main topics:
• Morphogenetic swarm robotic systems that deal with
the self-organization of swarm robots using genetic and
cellular mechanisms underlying the biological early mor-
2
phogenesis [32], [58], [84].
Morphogenetic modular robots where modular robots
adapt their configurations autonomously based on the
current environmental conditions using morphogenetic
principles [62], [63].
• Developmental approaches to the design of the body or
body parts, including sensors and actuators, and/or, design of the neural network based controller of robots [35],
[52]. Note that in epigenetic robotics, autonomous mental
development can be seen as an incremental, on-line,
and open-ended autonomous learning process situated in
physical and social environments. The first neural structure, as well as a basic intrinsic motivation system, which
enables robots to learn autonomously, is genetically hardwired as a result of neural morphogenesis (neurogenesis).
We believe that developmental robotics should include both
morphogenetic robotics and epigenetic robotics. The former is
mainly concerned with the physical development of the body
and neural control, whereas the latter focuses on the cognitive
and mental development. The body morphology, as well as the
neural structure of the robots are a result of morphogenetic
development, on which mental development is based through
interaction with the environment. The relationship between
morphogenetic robotics, epigenetic robotics and developmental robotics is summarized in Fig. 1.
•
ate intelligent behaviors with the help of the robot morphology
using a simple controller, and has not paid sufficient attention
to the developmental aspects of morphology.
A brief introduction to biological morphogenesis and its
computational models are presented in Section II. A metaphor
between swarm robotic systems and multi-cellular systems
is described in Section III, where a gene regulatory model
is used for self-organizing multiple robots to form complex
shapes. Related issues such as how to represent and form
complex shapes without a global coordinate system are also
discussed. Section IV presents our idea of using a gene regulatory network model for self-reconfigurable modular robots,
followed by Section V, where the developmental approach to
evolutionary co-design of the body and controller of robots or
robot parts (e.g., a robot arm / hand for object grasping) is
discussed. Concluding remarks of this paper are provided in
Section VI.
II. M ULTI -C ELLULAR M ORPHOGENESIS AND ITS
C OMPUTATIONAL M ODELING
A. Biological Morphogenesis and Metamorphosis
Morphogenesis of animals can be divided into early embryonic development and later embryonic development [27].
Early embryonic development typically involves cleavage,
gastrulation, and axis formation, while later embryonic development is mainly responsible for the development of the
nervous systems, starting with the segregation of neural and
glial cells from the ectoderm germ layer [80]. An example
of morphogenesis of nematostella vectensis is illustrated in
Fig. 2.
Fig. 2. Morphogenesis of nematostella vectensis. The development stages
are: Egg (A), morlula (B-F), blastula (G), gastrula (H), planula (I-J), and polyp
(K-L). Taken from [53].
Fig. 1. Relationships between morphogenetic robotics, epigenetic robotics
and developmental robotics. Developmental robotics includes both morphogenetic robotics and epigenetic robotics, and morphogenetic robotics and
epigenetic robotics are closely coupled not only directly in that the body plan
and nervous system are the basis of cognitive development, but also indirectly
through the environment.
Other closely related terms are evolutionary robotics [79]
and morphological computation (also known as morphological
robotics) [73]. Traditionally, evolutionary robotics is concerned with the design of robot controllers using evolutionary algorithms, which takes the phylogeny into account.
Complementary to evolutionary robotics, where the role of
robot morphology is largely neglected in designing intelligent
behaviors, morphological robotics was targeted for connecting
brain, body and environment in robot design. Unfortunately, it
appeared that morphological computation advocates to gener-
Metamorphosis is another interesting stage of biological
development. There are two types of metamorphosis, namely,
incomplete and complete metamorphosis. For organisms underlying incomplete metamorphosis, there are three developmental stages, in which nymphs look similar to adults.
In contrast, organisms that undergo complete metamorphosis
have four developmental stages, in which the shape of the
organisms changes drastically. Fig. 3 illustrates incomplete and
complete metamorphosis of insects.
Both multi-cellular morphogenesis and metamorphosis are
under the control of gene regulatory networks. When the
DNA is expressed, information stored in the genome is transcribed into mRNA and then translated into proteins. Some
of these proteins are transcription factors that can regulate
the expression of their own or other genes, thus resulting
in a complex network of interacting genes termed as a gene
3
abstraction models have also been used for modeling development, such as the L-systems [55] and grammar trees [30].
Generally speaking, the regulatory dynamics in a unicellular
cell can be described by a set of ordinary differential equations.
For example, the mathematical model of gene expression with
autoregulation can be described by:
Fig. 3.
(a) Incomplete and (b) complete metamorphosis.
regulatory network (GRN). New findings in the recent years
suggest that some previously so-called non-coding genes are
transcribed into small RNAs [59], which can downregulate
the expression of genes through e.g., RNA interference, as
sketched in Fig. 4. However, most computational GRN models
have not yet taken such effects explicitly into account with
few exceptions [26], [29]. In the following, we will discuss
computational modeling of GRNs and show how these models
can be used for understanding biology and solving engineering
problems.
d [R]
= −γR [R] + αR H([P ]),
(1)
dt
d [P ]
= −γP [P ] + αP [R],
(2)
dt
where, [R] and [P ] are the concentration of mRNA and protein,
respectively, γR and γP are the decay rate of the mRNA and
protein, αR and αP are the synthesis rate of the mRNA and
protein, and H(X) is the Hill function. If the autoregulation
is a repression, also known as negative autoregulation, the Hill
function can be described by
β
,
(3)
+ xn
and if the autoregulation is activation, the Hill function can be
written as:
β xn
Ha (x) = n
,
(4)
θ + xn
where β is the activation coefficient, θ is the threshold, and n
is the Hill coefficient.
For describing the morphogenesis of multi-cellular organisms, the interaction between the cells and its influence on
gene expression dynamics must be taken into account. Mjolsness et al. [66] has suggested a generalized GRN model that
considered diffusion of transcription factors among the cells:
" ng
#
X
dgij
jl
= −γj gij + φ
W gil + θj + Dj ∇2 gij ,
(5)
dt
Hr (x) =
θn
l=1
Fig. 4. An illustration of the gene expression process. Coding genes are
first transcribed into mRNA, and then translated into proteins, which can
have cellular and/or regulatory functions. Some so-called non-coding genes
can also transcribed into small RNAs that can downregulate or fully switch
off the expression of some genes through transcriptional or posttranslational
interferences.
B. Computational Modeling of Developmental Gene Networks
To understand the emergent morphology resulting from
the interactions of genes in a GRN, reconstruction of gene
regulatory pathways using a computational model has become popular in systems biology [11]. A large number of
computational models for GRNs have been suggested [15],
[20], which can largely be divided into discrete models, such
as random Boolean networks and Markovian models, and
continuous models, such as ordinary differential equations and
partial differential equations. Sometimes, GRN models also
distinguish themselves as deterministic models and stochastic
models according to their ability to describe stochasticity in
gene expression. Note that in artificial life, a few high-level
where gij denotes the concentration of j-th gene product
(protein) in the i-th cell. The first term on the right-hand
side of Equation (5) represents the degradation of the protein
at a rate of γj , the second term specifies the production of
protein gij , and the last term describes protein diffusion at
a rate of Dj . φ is an activation function for the protein
production, which is usually defined as a sigmoid function
φ(z) = 1/(1 + exp(−µz)). The interaction between the genes
is described with an interaction matrix W jl , the element of
which can be either active (a positive value) or repressive
(a negative value). θj is a threshold for activation of gene
expression. ng is the number of proteins. An illustration of
cell-cell interactions is provided in Fig. 5, where gene 1 of cell
1 is activated by its own protein and repressed by the protein
produced by gene 1 of cell 2 through diffusion. Similarly, gene
2 of cell 1 is activated by its own protein, and repressed by
the protein of gene 2 of cell 2 through diffusion.
C. Applications of Computational Models of GRN
In addition to reconstruction of gene regulatory pathways
based on biological data [85], computational models have
widely been used for analyzing the dynamics of GRNs,
particularly regarding robustness of GRN motifs, synthesizing
in silico typical regulatory dynamics such as bistability and
4
ical development in artificial life [89], designing complex
structures [91], and amorphous computing [8], to name a
few. Obviously, all the three areas of morphogenetic robotics
involve in computational models of biological morphogenesis,
which will be elaborated in the following sections.
III. M ORPHOGENETIC S WARM ROBOTIC S YSTEMS
A. Swarm Robotic Systems
Fig. 5.
Illustration of cell signaling in a multi-cellular system.
sustained oscillation, and designing engineered systems [16],
including morphogenetic robotics that will be discussed in
greater detail in the following sections.
1) Analysis of GRN Motifs: It is believed that GRNs can
be analyzed by examining the structure and function of a
number of wiring patterns, known as network motifs, such
as auto-regulation, feedforward loops and feedback loops [1].
Recently, the role of feedback loops, in particular, the coupling
of feedback loops and its relationship to the robustness of resulting dynamics of the network motifs has received increasing
attention [14], [51], [94].
The cis-regulation logic also plays an important role in the
dynamics and functionality of GRNs. A systematic investigation of control logic in gene regulation has been reported
in Schilstra and Nehaniv [81], which suggested that networks
consisting of competitively binding activators and repressors
can be controlled more robustly.
2) In silico Synthesis: In silico synthesis of typical regulatory dynamics can offer us insight into how nature has
shaped the evolution of regulatory motifs [25], [72]. In Knabe
et al [46], a GRN was used for evolving biological clocks
in the presence of periodic environmental stimuli, where
both the number and activation type (activating or repressive)
of regulatory units of each gene were subject to evolution.
They reported that the evolved clock tends to be robust to
perturbations that evolution has experienced. Jin and Sendhoff [41] investigated the influence of the genetic encoding
scheme as well as the activation function used in the gene
regulatory model of a relaxation oscillation circuit. Their
results suggested that evolving sustained oscillation using a
step function as the activation function is much easier than
using a Hill function. Most recently, it has been found that
robust motifs can emerge from in silico evolution without an
explicit selection pressure [40]. In [40], it has been found
that there is an inherent trade-off between innovation and
robustness in a feedforward Boolean model of genotypephenotype mapping [38], which, interestingly can be resolved
in a dynamic gene regulation model [42].
3) Artificial Embryogeny: A large body of research has
been reported on simulating biological development in computational environments [89]. Motivations of building models for artificial embryogeny include understanding biolog-
A swarm robotic system is a multi-robot system consisting
of a large number of homogeneous simple robots. Swarm
robots are often used to fulfill tasks that are difficult or even
impossible for a single robot, especially in the presence of
uncertainties, or with incomplete information, or where a
distributed control or asynchronous computation is required.
Compared with centralized systems, swarm robotic systems
with a distributed control are believed to be flexible, robust,
and adaptive for tasks that are inherently distributed in space
and/or time. Typical applications of swarm robotic systems
include group transport, foraging, shape formation, boundary
coverage, urban search and rescue, and unknown environment
exploration. However, designing a decentralized control algorithm for swarm robotic systems has been a challenging
task [60], [12].
B. A Metaphor between Swarm Robotic Systems and MultiCellular Systems
1) The Cell-Robot Mapping: The basic idea in applying
genetic and cellular mechanisms in biological morphogenesis
to self-organized control of swarm robots is to establish a
metaphor between a cell and a robot. In other words, it is
assumed that the movement dynamics of each robot can be
modeled by the regulatory dynamics of a cell. In [32], [39],
[61], the location and velocity of the robots are described by
the protein concentration of a few genes whose expression is
influenced by each other. Typically, for a robot in a threedimensional space, three proteins are used for denoting the
robot’s position, and three for the velocity. Note however
that the mathematical definition of the protein concentrations
standing for position and velocity of the robots do not satisfy
the exact physical relationship between position and velocity.
Fig. 6 shows multiple robots in a field, each represented by
a cell, where the robots are represented by cells containing a
virtual DNA in a field.
Keeping the metaphor between the cells and the robots in
mind, the movement dynamics of each robot can be described
by a GRN model, where the concentration of two proteins of
type G represents the x and y position of a robot, respectively,
and that of the proteins of type P representing the analog of
the velocity.
dgi,x
dt = −azi,x + mpi,x
(6)
dgi,y
dt = −azi,y + mpi,y
dpi,x
dt
dpi,y
dt
= −cpi,x + kf (zi,x ) + bDi,x
= −cpi,y + kf (zi,y ) + bDi,y
(7)
where i = 1, 2, ..., n. and n is the total number of robots (cells)
in the system. gi,x and gi,y are the x and y position of the i-th
5
Fig. 6. A swarm robotic system represented by a multi-cellular system.
Each circle represents a cell or a robot, and the dashed large circle denotes
the neighborhood of a cell/robot (shaded), to which information can be passed.
robot, respectively, which corresponds to the concentration of
two proteins of type G. pi,x and pi,y are the concentration of
two proteins of type P, which denotes the velocity-like property
of the i-th robot along the x and y coordinates, respectively.
Di,x and Di,y are the sum of the distances between the i-th
robot and its neighbors. In the language of the multi-cellular
system, it is the sum of the concentration of protein type G
diffused from neighboring cells. Mathematically, we have:
Di,x =
Ni
X
j
Di,x
, Di,y =
Ni
X
j
Di,y
,
(8)
where Ni denotes the number of neighbors of robot i, and
j
j
Di,x
and Di,y
are the protein concentrations diffused from
neighboring robot j received by robot i, which is defined as:
(gi,x − gj,x )
j
Di,x
=p
(gi,x − gj,x )2 + (gi,y − gj,y )2
,
(9)
(gi,y − gj,y )
(gi,x − gj,x )2 + (gi,y − gj,y )2
.
(10)
The diffusion term in the regulatory model simulates the
cell-cell signaling in multi-cellular systems. For a swarm
robotic system, this entails that each robot is able to detect
the distance to its neighboring robots, which is practical and
easy to realize.
2) Morphogen Gradients for Target Shape Representation:
In biological morphogenesis, morphogen concentration gradients control cell fate specification and play a key role in understanding pattern formation [5]. In the present gene regulatory
model for shape formation of swarm robots, the target shape
information is also provided in terms of morphogen gradients,
which is defined by fz in Equation 7. For two-dimensional
target shape, f (zi ) can be defined as follows:
f (zi,x ) =
f (zi,y ) =
1−e−zi,x
1+e−zi,x
1−e−zi,y
1+e−zi,y
(11)
where zi,x and zi,y are the gradients along x-axis and y-axis,
respectively, of an analytic function h, which is described as:
zi,x =
N
P
j=1
j=1
j
Di,y
=p
where h defines the shape the robots should form.
The above GRN makes it possible for the swarm robots
to form shapes that can be described by an analytical function. There are potentially three problems with this way of
shape representation. First, the complexity of the shapes is
limited. Second, the system needs a global coordinate system
for describing the shapes, which poses a big problem for
decentralized systems. Third, the shape can be formed only
on a predefined location. To address these issues, parametrized
shape representation models, such as are Bézier, B-Spline and
non-uniform rational B-Spline (NURBS) can be used.
NURBS [75] is a mathematical model commonly used in
computer graphics and design optimization for generating and
representing curves and surfaces. NURBS can offer two unique
features for multi-robot shape formation. First, it provides
a common mathematical form for both standard analytical
shapes and free-form shapes. Second, it is a parametrized
representation that is independent of an absolute coordinate
system. Once the parameter in the NURBS curve is fixed, a
corresponding point on the NURBS curve can be determined
without a global coordinate system. The basis functions used
in NURBS curves are defined as Bj,q (u), where i corresponds
to the j-th control point, and q is the degree of the basis
function. A NURBS curve can be defined as the combination
of a set of piecewise rational basis functions with N +1 control
points pj and the associated weights wj as follows:
∂h
∂h
, zi,y =
∂gi,x
∂gi,y
(12)
c(u) =
pi wj Bj,q (u)
j=1
N
P
(13)
wj Bj,q (u)
j=1
where N is the number of control points, u is the parametric
variable, and Bj,q (u) are B-spline basis functions.
With the NURBS model for shape description, complex
shapes can be formed, refer to Section III-C for examples.
C. Illustrative Results on GRN-Based Swarm Robot SelfOrganization
In the experiments, the parameters in Eqn. (6) and Eqn. (7)
need to be determined. A straightforward way is to define
the parameters heuristically with the following condition being
satisfied so that the states of the dynamic system can converge
to the target shape:
m · k ≤ a · c, a, c, k, m > 0.
(14)
The proof of the convergence is provided in [32]. In addition,
b should also be larger than zero so that collisions between
the robots, possibly between a robot and an obstacle, can be
avoided.
A more desired approach to setting up these parameters
is to find a set of optimal parameters using an evolutionary
algorithm by minimizing the time and / or the total travel
distance for all robots to converge to the target shape, as done
in [32].
If NURBS is used for representing the target shape, parameter u in Eqn. (13) should be determined for each robot. During
the self-organization process, each robot will randomly pick
6
a value from {0, 1/n, 2/n, ..., 1}, where n is the number of
robots in the system, which is either assumed to be known, or
can be estimated as described in [31]. It is therefore possible
that different robots pick the same u value in the beginning
and thus will compete the same point on the target shape. In
this case, robots arrive later will try another u value until it
converges to a point on the target shape where no other robot
exists.
Simulation results where 17 robots are used to form a birdflocking shape are given in Fig. 7. The robots are randomly
distributed in the area in the beginning. A reference robot
is chosen through a competition process, during which the
robot that has the maximum number of neighbors wins.
Driven by the GRN-based dynamics, the robots will then
autonomously form the target shape. Snapshots showing 20
robots covering a boundary simulating that of the Brooklyn
Borough of New York City are provided in Fig. 8. A proofof-concept experiment has also been performed using E-Puck
robots. Fig. 9 shows a few snapshots of 8 E-Puck robots
converging to a capital letter “R”, refer to [61] for details.
One important concern in designing decentralized algorithms for self-organizing swarm robots is their robustness
in the presence of disturbances in the system as well as
in the environment. Extensive empirical results show that
the morphogenetic self-organization algorithm is robust to
changes in the number of robots, insensitive to noise in the
model parameters sensory measurements, and adaptable to
environmental changes such as moving obstacles [39].
Fig. 9.
Snapshots of 8 E-Puck robots forming the letter ’R’ [61].
in the context of pattern formation, can be embedded in
the robot dynamics in the form of morphogen gradients. In
pattern formation, the global shape can be described using
parametrized models such as a NURBS model that can represent both analytical and free-form shapes. The GRN model can
then generate implicit local interaction rules automatically to
generate the global behavior, which can be guaranteed through
a rigorous mathematical proof. Second, the morphogenetic
approach is robust to perturbations in the system and in the
environment. Third, it has also shown that the morphogenetic
approach can provide a unified framework for multi-robot
shape formation and boundary coverage [31], since the representation of the target shape is independent of a specific
global coordination system. Morphogenetic approaches to selforganization of collective systems can potentially be applied
to solving other engineering problems such as the topology
self-reconfiguration of communication networks [54].
IV. M ORPHOGENETIC M ODULAR ROBOTS FOR
S ELF -O RGANIZED R ECONFIGURATION
A. Reconfigurable Modular Robots
Fig. 7.
Snapshots showing the emergence of a pattern from 17 robots
similar to bird flocking [31]. (a) Random initialization; (b) Determination
of a reference robot (denoted by a star) through competition; (c) Emergence
of the target shape.
Fig. 8. Snapshots of 20 robots covering a boundary simulating that of the
Brooklyn Borough of New York City [31]. (a) Random initialization; (b) The
robot that first detects the boundary is chosen as the reference robot; (c)
Coverage of the boundary.
D. Intermediate Summary
Compared to existing approaches [36], the morphogenetic
approach to swarm robotic systems has the following advantages. First, the global behavior, i.e., the target shape
Self-reconfigurable modular robots consist of a number of
modules and are able to adapt their shape (configuration) by
re-arranging their modules to changing environments [68].
Each module is a physical or simulated ’body’ containing a controller. Both physical modular robots, such as MTRAN [67] and Molecube [69], and simulated ’animats’, such
as Karl Sims’ virtual creature [87] and Framsticks [49] have
been constructed for reconfigurable robotic systems, refer to
Fig. 10. Modules in M-TRAN comprise two connected cubic
parts. The connection mechanism between the two cubic parts
allows the modules to perform basic motions such as lifting
or rotating. However, compared to single cubic mechanism,
the mandatory connection between the two cubic parts may
become a mechanical constraint. The modules in Molecube are
composed of two half-cubes on a diagonal plane. Each halfcube can swivel with respect to the other half, which is inspired
by the swiveling action. An advantage of Molecube modules is
their single cubic shape that can freely be attached or detached
to neighboring modules. However, the motion of the modules
often requires more free space around the module so that
the movement is not blocked. Although self-reconfiguration is
believed to be the most important feature of self-reconfigurable
robots, the ability to adapt their configuration autonomously
under environmental changes remains to be demonstrated.
7
position. During a parallel motion, a module moves from its
current position to a parallel position on its right. All joints of
the modules will stick out slightly to make enough free space
for modules to move. Climbing motion means that a module
moves to a diagonal neighboring position. Parallel motion and
climbing motion allow a module of CrossCube to move to any
position within the modular robot as long as the modules are
connected.
Fig. 10. Examples of physical and simulated modular robots. (a) M-TRAN,
(b) Molecube, (c) Karl Sim’ Virtual Creature and (d) Framsticks.
B. CrossCube - A Simulated Modular Robot
CrossCube [63] adopts a lattice-based cube design. Each
module in CrossCube is a cubical structure having its own
computing and communication resource and actuation capability. Like all modular robots, the connection part of the modules
can easily be attached or detached to other modules. Each
module can perceive its local environment and communicate
with its neighboring modules using on-board sensors.
Each CrossCube module consists of a core and a shell as
shown in Fig. 11(a). The core is a cube with six universal
joints. Their default heading directions are bottom, up, right,
left, front, and back, respectively. Each joint can attach to or
detach from the joints of its neighbor modules. The axis of
each joint can be actively rotated, extended, and return to its
default direction.
The cross-concaves on each side of the shell restrict the
movement trajectory of the joints, as show in Fig. 11(a). The
borders of each module can actively be locked or unlocked
with the borders of other modules, as shown in Fig. 11(b). The
length and angle of the lock mechanism can also be adjusted
on the boarders of the modules.
Fig. 11. Mechanical demonstration of CrossCube [63]. (a) The joints; (b)
The locks on the boundaries of the modules. (c) Rotation and extension of
the joints of the modules.
Basic motions of modules in CrossCube include rotation,
climbing and parallel motion. Fig. 11 (c) illustrates a rotation
movement of two modules. Parallel motion means that a
module moves to a next position which is parallel to its current
C. Self-Reconfiguration as Morphogenesis
The connection between reconfigurable modular robots and
multi-cellular organisms appears more straightforward. Each
unit in modular robots can be seen as a cell, and there are similarities in control, communication and physical interactions
between cells in multi-cellular organisms and modules in modular robots. For example, control in both modular robots and
multi-cellular organisms is decentralized. In addition, global
behaviors of both modular robots and multi-cellular organisms
emerge through local interactions of the units, which include
mechanic, magnetic and electronic mechanisms in modular
robots, and chemical diffusion and cellular physical interactions such as adhesion in multi-cellular organisms. Therefore,
it is a natural idea to develop control algorithms for selfreconfigurable modular robots using biological morphogenetic
mechanisms [100], [63]. In the following, we describe briefly
a recently proposed morphogenetic approach to designing
control algorithms for reconfigurable modular robots.
Similar to morphogenetic swarm robotic systems, each unit
of the modular robot contains a chromosome consisting of
several genes that can produce different proteins. The proteins
can diffuse into neighboring modules, through which local
communications between the modules can be established. The
concentration of the diffused proteins decays over time. The
target configuration of the modular robot is also defined by
morphogen gradients. The space in which the modular robot
is seated is divided by a set of grids, each of which will be
occupied by one CrossCube module. The morphogen gradient
can be either positive or negative. A positive morphogen
gradient means that the grid should be occupied by a module,
while a negative gradient suggests that the module in the grid,
if any, should be removed. A higher value of morphogen
gradient indicates a higher priority for the grid to be filled
by a module.
Different from the morphogenetic swarm robotic system
described in Section III, in which the target shape is fully
defined by a kind of maternal morphogen, each unit in the morphogenetic modular robot system can modify the morphogen
gradients by secreting either positive or negative morphogen
gradients, which is indispensable for adapting its configuration
to the current environment or task. As a result, each module
is able to attract or repel neighboring modules.
The attraction and repellent behaviors of the modules are
regulated by a GRN-based controller, which can adaptively
set the state of the modules to one of the following five
states, namely, ’stable’, ’unstable’, ’attracting’, ’repellent’, and
’repelled’. The transition relationships between the five states
of modules are given in Fig. 12. Refer to [63] for details of
state transitions.
8
respectively. a, b, and c are constant coefficients, which can
be determined e.g., using an evolutionary algorithm.
Based on the expression level of gA , the state of the module
can be regulated according to the following rules:

 unstable when gA < GA L
stable when GA L < gA < GA H
(17)
state =

attracting when gA > GA H
Fig. 12.
State transition of each module in CrossCube [63].
1) GRN-Based Pattern Transition: The state transitions are
controlled by a GRN model having two gene-protein pairs, an
attracting gene-protein pair (GA − PA ) and a repellent geneprotein pair (GP − PP ). We assume that the repellent states
always have a higher priority than the attracting states. As
a result, all the states triggered by attracting behaviors can
be overwritten by the states triggered by repellent behaviors.
The reason for this is that a grid having a repellent (negative)
morphogen gradient should be kept empty as long as migration
modules is still in need during reconfiguration.
2) Gene-Protein Pair for Attraction: The attracting geneprotein pair (GA − PA ) is used to control the transition
between ’attracting’, ’stable’ and ’unstable’ states as shown in
Fig. 12. At the initial stage of shape configuration, all modules
are set as unstable. After they are initialized with the target
configuration, modules located in the grids with an attracting
morphogen gradient become stable. For a newly stabilized
module, the gene expression level of its attracting gene GA
is initialized to be zero. Meanwhile, this module generates an
attracting protein PA for each empty neighboring grid that
has an attracting morphogen gradient. These grids become
’attracting’ to attract unstable modules to occupy them. Here,
PA is defined as:
ij
PAij = {AP ij , S i , CA
},
(15)
where PAij is the attracting protein generated by the i-th
module for its j-th neighbor. AP ij is the j-th neighboring
attracting grid of the i-th module. S i is the identification label
ij
of the i-th module, and CA
is the concentration of the protein
ij
PA , which equals to the morphogen gradient of AP ij . PA
can regulate GA in the same cell and can also diffuse into
neighboring modules to regulate GA of neighbors as well.
The dynamics of GA and PA can be described by the
following GRN model:
X
X
dgA (t)
= −a · gA (t) + b ∗
pA local − c ∗
pA rec , (16)
dt
where gA (t) is the gene expression level of GA at time
t. pA local and pA rec are protein concentrations of locally
generated protein and received protein from other modules,
where GA L is a negative threshold and GA H is a positive
threshold. According to Equation (16), gA falls P
below a
negative threshold GA LPwith the increase of c ∗
pA rec .
A higher value of c ∗
pA rec means that there are some
more important grids to be filled in. So the module needs
to change its state from stable to unstable and move to a
more important position following the attracting morphogen
gradient. An unstable module chooses a PA with the highest
concentration value from all the received attracting proteins.
Then the module migrates to the attracting position requested
by that PA . In order to guide the unstable modules to migrate
to their destination, each module can detect the proteins within
its local environment and choose the position with the highest
protein concentration as its destination. Once they reach their
destination, the unstable modules become stable.
PThe expression level of gA will be enhanced when b ∗
pA local increases, which means that the module has some
important neighboring positions to fill. So the module changes
its current state to the attracting state. The attracting modules
emit attracting proteins in the grid in which they sit, and
the emitted proteins will then diffuse into other modules.
The attracting module will become stable again once its
neighboring attracting positions are all occupied.
In summary, the gene-protein pair (GA − PA ) can regulate
each other by the GRN-based model described in Equations (16) and (17). More specifically, PA can regulate GA
through Equation (16), while GA can determine when PA
is allowed to diffuse into neighboring grids based on Equation (17). That is to say, only if the expression level of GA is
between GA L and GA H , PA can be generated; and only if
the expression level of GA is above GA H , PA is allowed to
diffuse.
3) Gene-Protein Pair For Repelling: The repellent states
are controlled by the repellent gene-protein pair (GP − PP ).
The repelling modules produce PP , which is defined as
PPij = {RP ij , S i , CPij },
(18)
where PPij is the repellent protein generated by the i-th
module for its j-th neighbor. RP ij is the j-th repellent grid
position around the i-th module. S i is the identification label
of repellent module i, and CPij is the concentration of the
protein PPij , which equals to a predefined positive constant.
As we mentioned before, when a stable module finds out that
some of its neighbors are located in a position with repellent
morphogen gradient, it changes its state to ’repellent’ and
switches the state of its neighbors to ’repelled’. If the repellent
module is triggered under this situation, RP ij is reset such
that PP can only repel the specific neighboring module that
is located in RP ij . If the repellent module is triggered by a
9
deadlock, RP ij is not reset because PP should be detected
by all the neighboring modules of the repellent module.
The gene expression level of gP is initialized to be the
morphogen gradient of the current grid position of the module.
It can be regulated by PP through the following equation:
P
dgP (t)
= d · gP (t) − e ∗ pP rec
dt
(19)
state = repelled when gP < GP L
where gp (t) is the gene expression level of the repellent gene
GP at time t, pP rec is the concentration of the received
repellent protein, GP L is a negative constant threshold and
d and e are constant coefficients.
When a module receives PP , the concentration of gP will
be reduced. If gp < GP L , the module changes its state
to ’repelled’. Obviously, modules with a lower morphogen
gradient are more easily to be repelled.
To summarize, PP can regulate GP through Equation (19).
GP can produce PP under the condition that GP is below
GP L and the module is blocked.
4) Look-Up-Table Based Configuration Representation:
Adaptation to environmental changes is of paramount importance in reconfigurable modular robots. Similar to analytical
or parametrized representation of the target shape in morphogenetic swarm robots, a mechanism is needed to define
and modify the target configuration of the modular robot.
Adaptation of the global configuration of the modular robot,
i.e., change in morphogen gradients, can be triggered by
local sensory feedback. Once a module receives such sensory
feedback, this information will be passed on to its neighbors
through local communication. In this way, a global change in
configuration can be achieved.
For the sake of simplicity, a number of basic configurations
for different environments can be predefined in terms of a
look-up-table for a given mission, for instance locomotion. For
such tasks, it is also assumed that each module is equipped
with a sensor to detect the distance between the module and
obstacles in the environment. An example of defining the
configuration of a vehicle is provided in Table I. In the table,
x, y, and z are 3D coordinates of grid positions, ML denotes
morphogen level and PID stands for position identification.
Additionally, we define some joints’ behaviors to enable the
vehicle to move, once the configuration is completed. Joints
can be identified by its PID and RD means joint rotate
direction.
TABLE I
A V EHICLE C ONFIGURATION
Positions
(x, y, z, ML, PID)
(0, 0, 0, 10, 0)
(1, 0, 0, 10, 1)
(2, 0, 0, 10,2)
(3, 0, 0, 10, 3)
(1, 0, 1, 10, 4)
(2, 0, 1, 10, 5)
(0, 0, 2, 10, 6)
(1, 0, 2, 10, 7)
(2, 0, 2, 10, 8)
(3, 0, 2, 10, 9)
(1,
(2,
(0,
(1,
(2,
(3,
(0,
(3,
(0,
(3,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
3,
3,
4,
4,
4,
4,
1,
1,
3,
3,
10, 10)
10, 11)
10,12)
10, 13)
10, 14)
10, 15)
-1, 16)
-1, 17)
-1, 18)
-1, 19)
Joints
(PID1, PID2, RD)
(0, 1, 0)
(2, 3, 1)
(6, 7, 0)
(8, 9, 1)
(12, 13, 0)
(14, 15, 1)
D. Illustrative Examples of GRN-Based Self-Reconfiguration
This section describes briefly a case study on using GRNbased controller to coordinate CrossCube modules for a locomotion task, in which the modular robot needs to traverse
through different environmental fields. A software is developed
to simulate the behaviors and interaction of CrossCube in a
physical world using C++ and the Physx engine from nVidia.
In the following experiment, the parameters of the GRN
models are setup as follows: a = 0.7, b = 1, c = 1, GA L =1, GA H =1, GP L =2, and CPij =0.7. The concentration of each
protein decays to 80% of its previous level when it diffuses
into a new grid.
Before showing the self-reconfiguration ability of the system
in a changing environment, we first perform a simple experiment to verify the effectiveness of the model. The modular
robot has a “block” configuration consisting of 16 modules,
which should convert into a vehicle-like pattern defined in
terms of morphogen level as shown in Table I. A set of
snapshots is provided in Fig. 13 to show a few intermediate
configurations toward the vehicle configuration realized by the
GRN-based model.
Fig. 13. Autonomous configuration of a vehicle from a rectangle based on
the GRN model [63].
To verify the model’s ability to re-configure the modular
robot to adapt to different environments, a simulation has
been performed where a vehicle needs first to move through
a narrow passage. Then, the robot must climb up a step to
move forward. The environment is defined using the size of
the modular robots as a unit: the wider passage is 7 units in
width, while the narrower passage is of 5.5 unit in width. The
height of the step is one unit. The reconfiguration is triggered
when any of the modules in the front detect obstacles. If
all front modules detect obstacles, a climbing reconfiguration
process will be activated. A number of snapshots showing the
reconfiguration processes are given in Fig. 14. More details of
the GRN-based modular robot system can be found in [63].
10
such as growing materials, adaptable structures, adaptable
sensors and actuators are still lacking.
Nevertheless, the role of development in brain-body coevolution cannot be overestimated, simply because in natural
evolution, development is an indispensable phase in which
organisms have to interact with the environment constantly
and find a way to survive. It has been found that development
can bias the evolutionary path considerably, as illustrated in
Fig. 15. In addition, it has been surmised that development
can also open up new opportunities for evolution [4], [78],
which has partly been verified in computational developmental
systems [42].
Fig. 14. A set of snapshots demonstrating a series of reconfigurable processes
during locomotion and climbing. The robot first adapted its width to the
narrow passage, then changed its configuration for climbing up a step, and
finally reconfigured itself into a vehicle again to move forward.
E. Intermediate Summary
The GRN model described above represents a hierarchical
approach to self-reconfiguration of modular robots, where one
layer defines the desired configuration of the modular robots
while the other layer organizes the modules autonomously to
achieve the desired configuration. Such a hierarchical structure makes it possible to separate the control mechanisms
for defining a target configuration from those for realizing
it, similar to biological gene regulatory networks [21]. In
response to the environment changes, the layer for defining
the robot configuration is able to adapt the target configuration,
based on which the second layer can re-organize the modules
autonomously to realize the target configuration.
V. M ORPHOGENETIC B RAIN AND B ODY D ESIGN FOR
I NTELLIGENT ROBOTS
A. Why Development?
The role of neural and morphological development in
designing intelligent robots has largely been neglected in
evolutionary robotics [56], although co-evolution of brain and
body has long been recognized both in [76] and artificial
life [92]. This situation has not been changed a lot to date
due to various difficulties in co-evolving the development
of body and brain. First, there are a lack of knowledge
about the developmental mechanisms in biology and a lack
of physically realistic environment [74]. Second, the influence
of artificial development on the systems performance is not
well understood. Although it is believed that the developmental
mechanism offers the possibility to evolve complex systems,
the performance advantage of such developmental systems
over non-developmental ones remains unclear. Finally, necessary hardware, which is of particular importance in robotics,
Fig. 15. Influence of development on selection directions. (a) Developmental
bias due to nonlinear genotype-phenotype mapping (taken from [77]), and (b)
Change of selection directions under developmental bias (taken from [4]).
B. Computational Models for Neural and Morphological Development
Various computational models have been suggested for
neural and morphological development [89], [34]. A large
body of research on modeling the growth of nervous systems was based on grammatical re-writing rules such as Lsystems [44], [10], [13] and grammar trees [30], [48]. In [17],
Kauffmann’s Boolean network was used for modeling the
structural development of dynamic neural networks. More
low-level models that consider cell-cell chemical interactions
through reaction and diffusion of morphogens have also been
employed for modeling neurogenesis [70], [23], [45], [18],
[65]. A recurrent artificial neural network was used for modeling the development of a spiking neural network for the
control of a Khepera robot [22]. In [24], the matrix rewriting
scheme suggested in [44] was applied to modeling neural
morphogenesis, which was co-evolved with neural plasticity
rules for controlling a mobile robot. A low-level GRN model
with chemical diffusion was adopted for evolving neurogenesis
for a hydra-like animats [41]. The weights of the developed
spiking neural networks were then further adapted using an
evolution strategy for generating food-catching behavior.
Similar computational models have also been suggested for
simulating morphological development. The main differences
11
may lie in the following aspects compared to those for neural
development. First, increasing attention has been paid to threedimensional models [19], [33], [90], [98], which plays an important role in modeling morphological development. Second,
physical cellular interactions are also modeled in addition to
the genetic regulatory mechanisms, such as adhesion repulsion
between the cells. Both sphere models [91] and spring-massdamper models [82] have been used.
Finally, efforts have also been made to simulate both neural
and morphological development using the same developmental
model, though most of them use a high-level developmental
model, such as the L-system [87], [49]. A Boolean genetic
regulatory network has been used for modeling both morphological parts such as sensor and actuator, and control part such
as control-neurons at a very high abstraction level [2].
So far, most neural networks generated by a developmental
model have very limited functionalities. In addition, most
developmental models of neural networks take only genetic
mechanisms, i.e., activity-independent development, into account. For the neural network to function, activity-dependent
development, which is responsible for synapse refinement,
is essential. The main processes in neural development is
summarized in Fig. 16. From the figure, we can see that early
development of nervous systems, such as neuron axon growth,
dendrite outgrowth and synapse maturation, which was usually
thought to be genetically regulated, are also considerably
driven by neural activity [83], [88], [93].
are activated, they will produce proteins either responsible for
cellular behaviors such as cell division, cell death, cell migration, and axon growth, or proteins regulating the activation
of the structural units, which are also known as transcription
factors (TFs). If a TF can only regulate the genes inside the
cell, it is then called an internal TF. If a TF can also diffuse out
of the cell and regulate the genes of other cells, it is termed as
an external TF. A TF can be both intracellular and intercellular.
An example of a chromosome in the cellular model for neural
development is provided in Fig. 17. From the figure, we note
that single or multiple RUs may regulate the expression of a
single or multiple SUs.
Fig. 17.
An example of chromosome for neural development.
Whether a TF can influence an RU is dependent on the
degree of match between the affinity value of a TF and that
of an RU. If the difference between the affinity values of a TF
and a RU is smaller than a predefined threshold , the TF can
bind to the RU to regulate. The affinity match (γi,j ) between
the i-th TF and j-th RU is defined by:
RU ,0 .
(20)
γi,j = max − affTF
i − affj
If γi,j is greater than zero and the concentration ci of the i-th
TF is above a threshold (ϑj ) defined in the j-th RU, then the
i-th TF influences the j-th RU.
Thus, the activation level contributedPby this RU (denoted
M
by aj , j = 1, ..., N ) amounts to aj = i=1 |ci , −ϑj |, where
M is the number of existing TFs. The expression level of the
k-th gene, that is regulated by N RUs, can be defined by
αk = 100
N
X
hj aj (2sj − 1),
(21)
j=1
Fig. 16.
Main processes in neural development driven by genetic and
environmental control situated in a physical environment together with the
development of the body plan.
C. A GRN Model for Neural and Morphological Development
The growth of the animat morphology is under the control
of GRNs and cellular physical interactions. Extended from the
cellular growth model for structural design, GRN models for
the development of a nervous system [41] and body plan [82]
of primitive animals have been proposed. In the genome of
the GRN models, each gene consists of a number of structural
units (SUs) proceeded by a number of regulatory units (RUs).
RUs can be activating (RU + ) or repressive (RU − ). When SUs
where sj ∈ (0, 1) denotes the sign (positive for activating and
negative for repressive) of the j-th RU and hj is a parameter
representing the strength of the j-th RU. If αk > 0, then the
k-th gene is activated and its corresponding behaviors encoded
in the SUs are performed.
A SU that produces a TF encodes all parameters related to
the TF, such as the affinity value, a decay rate Dic , a diffusion
rate Dif , as well as the amount of the TF to be produced:
A=β
2
− 1,
1 + e−20·f ·α
(22)
where f and β are both encoded in the SUTF .
A TF produced by a SU can be partly internal and partly external. To determine how much of a produced TF is external, a
percentage (pex ∈ (0, 1)) is also encoded in the corresponding
gene. Thus, pex A is the amount of external TF and (1 − pex )A
is that of the internal TF.
12
To make it easier for simulating the diffusion of TFs, cells
are put in an environment that is divided into a number of
grids. External TFs are put on four grid points around the
center of the cell, which undergoes first a diffusion (Eqn. 23)
and then decay process (Eqn. 24):
ui (t)
=
ui (t − 1) + 0.1 · Dif · (G · ui (t − 1)), (23)
ui (t)
=
min ((1 − 0.1 · Dic ) ui (t), 1),
(24)
where ui is a vector of the concentrations of the i-th TF at
all grid points and the matrix G defines which grid points are
adjoining.
The SUs encode cellular behaviors and the related parameters. The SU for cell division encodes the angle of division,
indicating where the daughter cell is placed. A cell with
an activated SU for cell death will die at the end of the
developmental time-step.
The above cellular model has been applied to simulate both
morphological and neural development [41], [82]. In the experiment to generate an animat like C. elegans, two prediffused,
external TFs without decay and diffusion are deployed in
the computation area (maternal morphogen gradients). The
first TF has a constant gradient in the x-direction and the
second in the y-direction. In the experiments, the GRN model
is initialized randomly, and the target of the evolution is to
evolve an elongated animate whose morphology is defined by
a rectangular shape. Without any hard constraints for stopping
cell division, we are able to evolve a GRN that results in selfstabilized cellular growth [82]. A few snapshots of the selfstabilized cellular growth process is provided in Fig. 18, where
the cellular system starts from two cells sitting in the middle of
the simulation area and reaches a dynamic stability at the end
of the development. In the figure, cells in light color are going
to divide in the next developmental step, and those in dark are
going to die in the next step. In another experiment, we use
a similar GRN model for simulating neural growth in hydra.
In the beginning, a few simulated stem cells are randomly
distributed in the body plan of the hydra-like animat. Then,
cells divide, migrate and axons grow so that the neurons are
connected [41]. Snapshots showing this growth process are
given in Fig. 19. The evolved GRN resulting in the neural
development in Fig. 19 is presented in Fig. 20, which is able
to generate the correct temporal activation sequence for cell
division, cell migration and axon growth.
D. A Conceptual Framework for Co-Evolving the Development of Robot Hand Morphology and Controller
It has been found that the morphology of the animal hands
has changed a lot to adapt to the needs of the animals during
evolution. Fig. 21 (a) shows a few examples of primate hands.
From the figure, we can see that they distinguish themselves
in both shape and length in the finger segments. Besides, it has
been hypothesized that particular behaviors, such as throwing
and clubbing, have played a key role in differences between
a hand of human beings and that of a chimpanzee [99], refer
to Fig. 21 (b).
The importance of co-evolving the development of hand
morphology and control in robotics is two-fold. On the one
Fig. 18. Self-stabilized cellular growth under the control of a GRN model
presented in [82]. (a) The system is initialized with two cells. (b)-(c): The
system grows as cells divide. (d) The growth is self-stabilized dynamically,
where the cells on light gray color will divide and those in dark will die. A
balance of cell division and cell death is accomplished under the control of
the GRN.
Fig. 19. Development of a nervous system using the GRN model in [41].
(a)A few stem cells are randomly distributed on a hydra-like body wall. (b)(d) Cells divide, migrate and axons grow. As the development goes on more
connections are built up.
hand, object grasping and manipulation with a robot hand is in
itself a challenging task in that such systems are usually highly
redundant. Existing work focuses on the design of the hand
controller for a given morphology [97], which is inefficient
when the shape of the objects changes considerably. A better
approach is to co-design the hand morphology and control in
a developmental manner, as illustrated in Fig. 22. In this way,
the shape and number of finger segments, the number fingers
and even the number of arms can be evolved together with
their controller.
Meanwhile, co-evolution of the hand morphology and control in a computational environment provides us a means
for understanding the phylogenetic changes in evolution of
animal hands. So far, brain-body co-evolution in computational
13
Fig. 20. The evolved GRN resulting in the neural development in Fig. 19.
SU: structural genetic units; RU: regulatory genetic units.
Fig. 22. A conceptual diagram for co-evolving the development of hand/arm
and control. Adapted from [37].
Fig. 21. (a) Examples of primate hands. (b) Differences between a human
hand and a chimpanzee hand.
environments has led to findings regarding the organizational
principles of nervous systems and the emergence of bilateral
symmetry in neural configuration [43], [71]. We expect that
different hand morphologies will emerge by evolving the
system for different behaviors.
VI. C ONCLUDING R EMARKS
This paper suggests a new field of robotics termed morphogenetic robotics, which focuses on employing genetic and cellular mechanisms in biological morphogenesis for developing
self-organizing, self-reconfigurable and self-adaptive robotic
systems, covering a wide range of robotic systems such as
swarm robotic systems, modular robots and intelligent robots.
Morphogenetic robotics, as epigenetic robotics, is a part of developmental robotics. While epigenetic robotics concentrates
on the mental development of robotic systems, morphogenetic
robotics focuses on the physical development of the body plan
and nervous system of the robots. Therefore, we believe that
developmental robotics should include both morphogenetic
robotics and epigenetic robotics.
Research on morphogenetic robotics is still in its infancy
and therefore many issues remain to be explored. First, many
genetic and cellular mechanisms underlying biological morphogenesis still remain elusive, and much work needs to be
done on reconstruction of spatio-temporal gene expression
patterns using computational models based on biological data.
In particular, the self-adaptation capability of the genetic
and cellular models to environmental changes used in morphogenetic robotics needs to be improved. The introduction
of hierarchical gene regulatory models suggests a promising
step toward this goal, but many details on autonomous selfadaptation based on sensory input are still unclear. Second,
the interactions between morphogenetic robotics and epigenetic robotics are largely unexplored. Obviously, the physical
and mental development are closely coupled, since neural
and morphological development lay the neuro-physiological
foundation for cognitive and mental development, and both
are constrained by the environment in which the robots reside.
Furthermore, research on developmental robotics should also
be performed taking evolution into account, as development
can not only bias the direction of evolution, but also enhance
evolvability [42]. Finally, morphogenetic robotics is currently
very much limited to computational simulations. Appropriate
hardware for morphogenetic robotics, including programmable
materials [3], [47] and adaptable sensors and actuators, is to
be studied.
ACKNOWLEDGMENTS
The authors would like to thank Hongliang Guo, Yuyang
Zhang, Lisa Schramm, Till Steiner, and Benjamin Inden for
the illustrative examples used in this paper. Y. Jin is grateful
to Edgar Körner and Bernhard Sendhoff for their support.
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